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Research Papers

Analysis of Unsteady Flows Past Horizontal Axis Wind Turbine Airfoils Based on Harmonic Balance Compressible Navier-Stokes Equations With Low-Speed Preconditioning

[+] Author and Article Information
M. Sergio Campobasso1

School of Engineering,  University of Glasgow, James Watt Building South, University Avenue, Glasgow, G12 8QQ, UKsergio.campobasso@glasgow.ac.uk

Mohammad H. Baba-Ahmadi

School of Engineering,  University of Glasgow,James Watt Building South, University Avenue, Glasgow G12 8QQ, UKm.baba-ahmadi@aero.gla.ac.uk

1

Corresponding author.

J. Turbomach 134(6), 061020 (Sep 04, 2012) (13 pages) doi:10.1115/1.4006293 History: Received July 10, 2011; Revised July 21, 2011; Published September 04, 2012; Online September 04, 2012

This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time-and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic views of HAWT in yawed wind. Left plot: top view; right plot: front view.

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Figure 2

Velocity triangles of HAWT blade section for positions labeled A to D in Fig. 1

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Figure 3

Harmonic motion of HAWT blade section corresponding to yawed inflow

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Figure 4

Amplitude of the first harmonic of the differential static pressure coefficient across a pitching flat plate: comparison of theoretical result and numerical predictions obtained with and without LSP

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Figure 5

Lift coefficient of 90% blade section over one revolution computed with TD and five HB analyses

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Figure 6

Hysteresis force loops of 90% blade section computed with TD and five HB analyses (line legend as in fig. 5): (a) lift coefficient, (b) drag coefficient, (c) pitching moment coefficient

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Figure 7

Pressure coefficient of 90% blade section computed with TD and five HB analyses: (a) real part, (b) imaginary part

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Figure 8

Skin friction coefficient of 90% blade section computed with TD and five HB analyses (line legend as in Fig. 7: (a) real part, (b) imaginary part

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Figure 9

Convergence histories of TD, HB and steady analyses for 90% blade section

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Figure 10

Lift coefficient of 30% blade section over one revolution computed with TD and five HB analyses

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Figure 11

Hysteresis force loops of 30% blade section computed with TD and five HB analyses (line legend as in Fig. 1): (a) lift coefficient, (b) drag coefficient, (c) pitching moment coefficient

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Figure 12

Pressure coefficient of 30% blade section computed with TD and five HB analyses: (a) real part, (b) imaginary part

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Figure 13

Skin friction coefficient of 30% blade section computed with TD and five HB analyses (line legend as in Fig. 1: (a) real part, (b) imaginary part

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Figure 14

Convergence histories of TD, HB and steady analyses for 30% blade section

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Figure 15

Lift coefficient of 30% blade section computed by TD analysis with and without low-speed preconditioning

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